Geometry and Lines: Master Shapes and Angles for Public Services

Question 1

What is the sine of an angle measuring 30 degrees?

Accepted Answer

0.707

Answer

0.5

Answer

1

Answer

√2

Question 2

Which shape exhibits rotational symmetry of order 4?

Accepted Answer

Square

Answer

Rectangle

Answer

Equilateral triangle

Answer

Isosceles triangle

Question 3

What is the formula for the area of a trapezoid with bases b1 and b2 and height h?

Accepted Answer

0.5(b1 + b2)h

Answer

(b1 + b2)h

Answer

b1h

Answer

0.5b1b2h

Question 4

Find the area of a right-angled triangle with a base of 6 cm and a height of 4 cm.

Accepted Answer

24 cm²

Answer

12 cm²

Answer

48 cm²

Answer

96 cm²

Question 5

Which transformation involves rotating a figure around a fixed point?

Accepted Answer

Rotation

Answer

Translation

Answer

Reflection

Answer

Dilation

Question 6

Identify the type of line segment that joins two points on a circle without passing through the center.

Accepted Answer

Chord

Answer

Tangent

Answer

Radius

Answer

Diameter

Question 7

Find the measure of an angle that is complementary to a 45° angle.

Accepted Answer

90°

Answer

22.5°

Answer

45°

Answer

135°

Question 8

Classify the following quadrilateral based on its properties: opposite sides parallel, opposite angles equal, diagonals bisect each other.

Accepted Answer

Parallelogram

Answer

Rectangle

Answer

Rhombus

Answer

Square

Question 9

Find the measure of an angle that is adjacent to a 135° angle and forms a straight line.

Accepted Answer

180°

Answer

45°

Answer

90°

Answer

135°

Question 10

Which property is NOT characteristic of a parallelogram?

Accepted Answer

Diagonals are perpendicular

Answer

Opposite sides are parallel

Answer

Opposite angles are equal

Answer

Diagonals bisect each other

Question 11

Classify the triangle with angles measuring 60°, 70°, and 50°.

Accepted Answer

Acute triangle

Answer

Right triangle

Answer

Obtuse triangle

Answer

Equilateral triangle

Question 12

Calculate the area of a circle with a radius of 5 cm.

Accepted Answer

25π cm²

Answer

50π cm²

Answer

75π cm²

Answer

100π cm²

Question 13

Which transformation is NOT an isometry?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 14

Identify the Pythagorean triple among the given options:

Accepted Answer

(3, 4, 5)

Answer

(5, 12, 13)

Answer

(6, 8, 10)

Answer

(7, 24, 25)

Question 15

What is the name of the point that divides a line segment into two equal parts?

Accepted Answer

Midpoint

Answer

Centroid

Answer

Incenter

Answer

Circumcenter

Question 16

Which method is valid for constructing the bisector of an angle?

Accepted Answer

Using a compass and ruler

Answer

Folding a paper along the angle

Answer

Using a protractor to measure half the angle

Answer

Drawing any line through the vertex of the angle

Question 17

Calculate the area of a rectangle with a length of 10 cm and a width of 5 cm.

Accepted Answer

50 cm²

Answer

25 cm²

Answer

15 cm²

Answer

100 cm²

Question 18

What is the volume of a cube with a side length of 3 cm?

Accepted Answer

27 cm³

Answer

12 cm³

Answer

9 cm³

Answer

81 cm³

Question 19

Which property is NOT true for a parallelogram?

Accepted Answer

All sides are equal

Answer

Diagonals bisect each other

Answer

Opposite angles are equal

Answer

Opposite sides are parallel

Question 20

What is the measure of an angle that forms a supplementary pair with a 60° angle?

Accepted Answer

120°

Answer

90°

Answer

30°

Answer

150°

Question 21

Which transformation results in a figure mapping onto itself?

Accepted Answer

Rotation

Answer

Dilation

Answer

Reflection

Answer

Translation

Question 22

What is the formula for the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

b² + c² = a²

Answer

c² - a² = b²

Answer

a² - b² = c²

Question 23

Which of the following is a regular polygon?

Accepted Answer

Octagon

Answer

Trapezoid

Answer

Rectangle

Answer

Parallelogram

Question 24

What is the order of rotational symmetry for a square?

Accepted Answer

4

Answer

2

Answer

8

Answer

6

Question 25

Which tools are used to bisect an angle?

Accepted Answer

Compass and straightedge

Answer

Compass only

Answer

Ruler only

Answer

Protractor only

Question 26

Which theorem states that the sum of the interior angles of a triangle is 180°?

Accepted Answer

Triangle Sum Theorem

Answer

Pythagorean Theorem

Answer

Angle Bisector Theorem

Answer

Exterior Angle Theorem